The remarkable HST datasets from the CANDELS, HUDF09, HUDF12, ERS, and BoRG/HIPPIES programs have allowed us to map out the evolution of the UV LF from z~10 to z~4. We have identified 5859, 3001, 857, 481, 217, and 6 galaxy candidates at z~4, z~5, z~6, z~7, z~8, and z~10, respectively from the ~1000 arcmin**2 area probed. The selection of z~4-8 galaxies over the five CANDELS fields allows us to assess the cosmic variance; the largest variations are apparent at z>=7. Our new LF determinations at z~4 and z~5 span a 6-mag baseline (-22.5 to -16 AB mag). These determinations agree well with previous estimates, but the larger samples and volumes probed here result in a more reliable sampling of >L* galaxies and allow us to reassess the form of the UV LFs. Our new LF results strengthen our earlier findings to 3.4 sigma significance for a steeper faint-end slope to the UV LF at z>4, with alpha evolving from alpha=-1.64+/-0.04 at z~4 to alpha=-2.06+/-0.13 at z~7 (and alpha = -2.02+/-0.23 at z~8), consistent with that expected from the evolution of the halo mass function. With our improved constraints at the bright end, we find less evolution in the characteristic luminosity M* over the redshift range z~4 to z~7; the observed evolution in the LF is now largely represented by changes in phi*. No evidence for a non-Schechter-like form to the z~4-8 LFs is found. A simple conditional LF model based on halo growth and evolution in the M/L ratio of halos ((1+z)**-1.5) provides a good representation of the observed evolution.
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